Friday, 15 July 2016

A Constellation of Warships II

Here, we will continue the discussion on space fleet composition and formations.

As mentioned in Part 1, one of the most important determinants of fleet composition and formation is the technologies in use. Spaceships will be designed to exploit the advantages offered by certain technologies, while mitigating side-effects and weaknesses.

The Grand Fleet at the Battle of Jutland

However, all that matters in practice is the difference in effectiveness of the technologies between the combatants, in other words, it's the relative strengths that matter.

An example would be propulsion technology. In a sufficiently advanced setting, a wide variety of nuclear, chemical and electric rocket engines might be available to mount on warships. The choice would affect the rate of travel, the effective range of fleets and more.

Isp vs deltaV

However, all warships will likely mount the drive best suited for combat, and what will matter then is the relatively minor differences in performance that result from equipment designed and built by different groups, instead of the huge differences between the various options.

We'll now go down a list of various factors that will affect fleet compositions and formations:

Pixel-formations

As established in a previous series of posts, stealth in space is a non-negligible possibility. Its importance increases the closer a setting is to modern-day technology.

In the default scifi setting, spaceships put out incredible amounts of power to move around quickly. This does not mean that stealth is not a factor. A pixel-formation is recommended.A 'perfect' or single-pixel-formation is a close arrangement of spaceships, made so that all of the fleet's detectable emissions lie within a single pixel of the sensors you are trying to evade. A pixel-formation is two-dimensional, as the depth of the formation has no effect on the detectability, at extreme ranges. The perfect pixel-formation allows the number of spaceships inside a fleet to be obscured from the enemy. Since exhaust plumes cannot be distinguished, it can even help prevent the enemy from knowing the mass and performance of the spaceships in formation. A pixel-formation is possible thanks to the finite angular resolution of a sensor. This formula gives the maximum separation of spaceships within a pixel formation at which they cannot be distinguished:

Pixel width: Distance * tan(69.9 * Wavelength /Diameter)

Distance is the separation between sensor and fleet. Wavelength is that of the Diameter is that of your sensor array. A single sensor is limited to the radius of its mirror, in the handful of meters, but an array can create a 'virtual telescope' of radius equal to their separation.

ALMA links with other observatories to create an Earth-sized Virtual Telescope

We can quickly see that this is only useful against individual spaceships or at interstellar distances. Sensors can easily be placed at opposite sides of an orbit to create a virtual telescope thousands of kilometers across, able to pinpoint the location of a spaceship down to the millimeter. In combat, doing so might not be so simple.If multiple spacecraft maintain a separation within two pixel-widths, then their signal will form a large, uniform spot on the sensor. This is a more practical application of the pixel formation, but with reduced effectiveness: unlike a single pixel formation, your enemy will know that multiple spacecraft are present, even if the exact number cannot be determined. Closely Distributed SignalsIn situations where detection of spacecraft is not a foregone conclusion, it would be sensible to reduce the opponent's ability to detect spacecraft using distributed signals.As mentioned in Stealth in Space, the difference in the ranges at which a sensor can detect a spaceship when it is under power or drifting cold is great. In the examples, calculated, it was the difference between being spotted across the Solar System (several hundred million km) or staying undetected a day away from your opponents (one million km or less). This leads to a situation where, for spacecraft that do not continuously accelerate and have non-negligible travel times, they are only detected when the engines are running. Switching the engine on and off would be seen by a sensor as a lightbulb appearing and disappearing from sight.

Like twinkling stars...

Due to the way motion works in space, you cannot change your trajectory without producing thrust. As noted, producing thrust makes you detectable. The immediate conclusion is that your trajectory while undetected can easily be deduced from your motion at the end of your engine burn. It can be as simple as connecting the dots and following the vector they trace.However, a fleet in space can defeat an opponent's ability to predict their motion in this manner. The first method relies on distributed signals. Closely distributed signals are the result of spaceships in very close formation, alternating the firing of their engines in a random manner. They would be seen as a cluster of signals appearing and disappearing in an unpredictable manner. This alone is not enough to prevent their trajectory from being predicted.

Explanation of the effect of closely distributed signals

The figure above explains how closely distributed signals can throw off predictions on a fleet's trajectory. This method can be combined with 'cold engines' that are used to re-position spaceships within a fleet, a task well suited to their low efficiency.Closely distributed signals is very effective in defeating missiles with low deltaV, so unable to catch up to spaceships if shot onto an intercept course far from their target's actual trajectory. It is also essential in evading 'stealth' projectiles that cannot be detected until very close, but cannot alter their trajectory either. Remotely Distributed Signals. Here, we rely on the fact that sensor platforms cannot cover the sky with very sensitive narrow-angle sensors, the sky cannot be scanned instantly and all data cannot be correlated confidently within a short span of time.

1 degree FoV is quite large by today's standards

To exploit these limitations, the fleet's individual spaceships attempt to depart on very different trajectories, converging on their target only by the end of their trip. Maximal separation puts them millions, if not hundreds of millions of kilometers apart, with their emissions literally coming from all corners of the sky. This 'maximum remoteness' technique might be able to prevent your target from even recognizing the signals as belonging to an attack, but it will cost your fleet much more deltaV to perform, and your total trip time will have to be very rigidly defined so that all spaceships meet at the same point.Mid-Remote Distributed Signals. Mid-remote distributed signals is more situational. It is to be used against an opposing fleet, with a limited number of sensors. Narrow-angle sensors only cover a small section of the sky. The objective then is to distribute the fleet's spaceships over an area larger than that covered by a single narrow-angle sensor.

Your opponent will be forced to scan the entire section of the sky your spaceships are possibly in. This means that the sensors cannot continuously cover your spaceships' likely positions. For example, if a 0.5 degree FOV sensor was looking at targets approximately 10 million km away, then it can only cover a section of the sky 87260 by 87260km across. If the spaceships in a fleet are distributed over an area 150000km in radius, then the sensor can only ever see 10.8% of the fleet at any one time. If the sensor wishes to pick up details 10m across, then it requires 76 trillion pixels, or a CCD plate 8.7 meters wide, consisting of 1 micron sized pixels.

Twice the performance, thrice the efficiency of the previous Titan X

A 10 GPU stack of Nvidia's GTX1080 can handle 100GB/s. The CCD will produce 152 TB images of its FOV. Therefore, full scans of the fleet's mid-remote distributed signals area will be completed every four hours ... and this is without any further analysis of the data. Entire insertion burns can go unseen. Even a gentle 0.01G acceleration for 4 hours will push a spaceship to 1412m/s. If it is travelling at a closing velocity of 20km/s, and it performs no other burns, by the time it is detected by wide-angle sensors at a distance of 1 million km, it would be out of position by 635000km. It would evade any pre-positioned kinetics, and would attack at a 32.4 degree angle.In return, your opponents will be forced to massively increase processing bandwidth, accept lower details or reduce the scanned area and take the risk of being surprised at much shorter ranges, where wide-angle sensors start picking up cold spaceships. In return, you will focus on higher acceleration spaceships that perform their burns in shorter periods of time, and on 'spoofer' spaceships that are able to distance themselves from the fleet stealthily, perform a visible burn, then slowly cancel the velocity gained with 'cold engines'. This will massively increase the area sensors will have to cover. Lasers and angles

The most mass-efficient configuration for a spaceship is one where all armor is concentrated in the likely direction of the threat will be. In other words, the front. This design philosophy is most prominent in tank design. Taken to its extreme, front-loaded armor will end up forming a 'faceplate'; a thick plate on the front of the spaceship. However, the freedom of movement in space precludes this from being a viable design.The reason is that in a setting where lasers are an effective weapon, opponents can position themselves far from the Hohmann corridor or other likely trajectories, and fire lasers at an angle.Firing at an angle by-passes front-loaded armor. The only way to counter this for certain is to extend the armor past the front of the spaceship and over the sides. However, increasing the surface area covered by armor translates into a greater mass penalty. This has to be compensated for by reducing the thickness of side armor, reducing the mass of the frontal armor through sloping, going for an 'all-or-nothing' armor scheme where voluminous propellant tanks are not protected, accepting lower deltaV to use denser propellants with lower volumes, ect...There has to be a balance between the angles of attack your armor protects from, and the percentage of your payload you are willing to dedicate to armor. The balance point is determined mostly by where you expect your enemy to be. In practice, spacecraft will be very well defended against attacks directly from the front, thanks to sloping. Against a small arc to the front, the full thickness of frontal armor will be put to use. A wide angle to the sides is covered by thinner armor. The rear is unarmored, as it would be prohibitive to cover the propellant tanks and it leaves room for radiators and nozzle openings.

Arcs defined by armor coverage

The frontal arc is mostly defined by the likely positions of targets the warship will be able to detect and orient itself towards them, before an engagement. This will correlate with the field of view of narrow-angle sensors.The lateral arc is mostly defined by the rocket engine's performance, as a more efficient engine will allow the spaceship to mount more armor while still reaching the same deltaV targets. The rear arc is open to space and contains sacrificial, expendable and unprotectable equipment. The objective of an attacking warship becomes its positioning at an angle from the target's nose large enough for it to negate sloping, or even better, attack the side armor. If it can catch the rear arc, then the target was grossly out of line and would have been defeated, with or without armor protecting it.With this objective in mind, fleets will arrange themselves into offensive or defensive formations. There are infinite variations possible.

Each vertex is a spaceship.

One example of an offensive formation is a pyramid with one target spaceship from the opposite fleet, singled out, at its tip, and the attacking craft forming the base. The target cannot point its armor at any of the attacking craft without exposing its sides to another. An example of a defensive formation is the shield-stack. Spaceships arrange themselves into very close formation, closing off the innermost ships from attack from all angles, and reducing the fleet's exposure to only the outermost ships. Depending on the numbers involved, it can be a simple 4-ship diamond, up to a thousand-ship sphere with optimal exposed-to-protected ratios. The laser angling objective can be approached temporally as well as spatially. If a cluster of spaceships opens fire on the target from one direction, forcing it to point towards them, this creates an opening for a spaceship that escaped detection using distributed signal techniques to perform a flank attack at a very favorable angle.

Not necessary to have fun

The battle should be dynamic, and opposing fleets will change their strategies and formations to defeat those employed by the enemy. A shield-stack must evolve into a 'puffer-fish' formation to defeat undetected stealth craft, and in return becomes vulnerable to missiles as it cannot manoeuvre effectively. Once dispersed, individual spaceships will focused by a pyramid, requiring a reverse-pyramid counter-attack to even the odds, and so on...We will continue in part III.

14 comments:

A couple minor corrections to begin with: First, even a 1 000 000 km baseline for an array will only permit a resolution on the order of meters per pixel, not millimeters.Second, the baseline distance between the most remote posts of an array is the equivalent of the DIAMETER of a single telescope, not the radius.Third, possibly not an error, but a discrepency... could you cite the reference for your formula? According to my sources, pixel width is simply Distance*Wavelength/Baseline. I do not recall any mention of tangent in the formula, and the baseline is the diameter, not the radius.

It is worth noting that units in an array need to be able to communicate with one another for interferometric telescopy to work. This means that you would need a central relay station if the remote units were on opposite sides of orbit. A large baseline difference also determines a minimum lag time for image processing.Also, recall that baseline only improves resolution. Actual sensitivity requires actual detector surface area. If you have a 5" telescope on Earth, and another on the moon, you will have fairly decent resolution... but you will not be able to actually see much of anything smaller than a large planet.

Finally, the tactic of using a large baseline to overcome sloped armour is limited to either very close combat distances, or to resources spread throughout a solar system... or favouring attacks from distal orbits (orbits further away from a star) over proximal orbits (orbits closer to a star). For example, platforms on opposite sides of a 1 AU orbit would not likely be able to defeat the armour slope of a vessel in a 2 AU orbit.Another consideration is that slope can be employed in three dimensions. This means that side armour can also be sloped... although not quite as significantly.

I made a mistake writing radius. I made calculations with the diameter, so it's a typo. Thanks for spotting it.

I used the angular resolution formula from this page: [https://en.wikipedia.org/wiki/Angular_resolution] and converted it to use degrees instead of radians, and to calculate a resolution in meters instead of radians. tan(angle)*distance comes from right angle equations, for calculating the length of the far side if you know the length of the near side and an angle.

Most situations described here assume interplanetary combat, between planets with mature detection and defense capabilities. The maths is still valid for other situations, so if you are forced to use 5 inch telescopes to spot space warships, then resolution becomes a major issue.

You are correct about the large baselines, but as noted in the 'remotely distributed signals' section of this post, deviating by hundreds of thousand of kilometers from your trajectory to attack from angles of 30, 40, 90 degrees even, is entirely possible. Another point to consider is that effective range is the fixed constant in play, while spaceships can be moved around. If combat ranges are millions of kilometers, then achieving useful attack angles takes days of stealthy drifting. If it is only 1000km, then it can be achieved in a matter of minutes, even at low accelerations.

The diagram I made for angles is extremely simplistic when it comes to design possibilities. I can think of extreme-range x-ray laser platforms having nothing but a rather thin nose-cone for protection, while a short-ranged brawler using efficient optical lasers would instead have 135 degree thick cover of multi-faceted laser armor, covered by a replaceable thin scaffolding of whipple shield plates that would give it a much thicker appearance than it actually is....

Sorry, my mistake. I recalculated the figures with the formula I found (same site as yours, actually), and came out with 0.122 mm (this is the length of a curve at a constant distance... convenient because, at such distances, the curve is almost indistinguishable from a straight line over short arcs). It appears that I was confusing the approximation equation (R=wavelength/B), which does not include the distance factor, with the"full" equation including both the distance factor and the 1.22 constant. I assume that the 1.22 constant (rounded) comes from the calculation that your (tan) 69.9 figure is based on... unless we got to the similar values just by chance. Anyway, I think I must have been confusing the calculation for the 1 000 000 km baseline with another array calculation that I had done for another site. I remember that I HAD calculated the required baseline for a resultion on the order of mm, but I thought that had been for alarger baseline.

The reference of a 5" telescope was merely to illustrate that baseline does not affect sensitivity. It can be easy to believe that if an array has the resolution of a giant telescope, it would otherwise be just as good as that giant telescope. I was only pointing out that this is not the case.Interestingly, I saw a comment that to perform the interferometry for an array "several" telescopes are required. Wiki does not explain this comment, but it implies that you need more than just the simple baseline. Currently, I am assuming that this is because the baseline will only help for resolution in a single dimension, so you will need at least a third telescope to ensure resultion of non-aligned segements. Still, "several" can be a somewhat confusing reference.This actually brings up an interesting problem: you can't just stick a telescope in space. If you are in a solar system, you are going to have to put in in orbit around something. You can make a lunar/terrestrial baseline fairly simply, but then you need a second set of baselines of equally great distances from the first two points. This means a giant polar orbit, which is not going to provide a stable baseline distance between the other telscope sites. Doable, but you need more calculation time.

Yes, your strategies could work at relatively short ranges. I might be mistaken, but I thought that I had specified the problem with the long ranges, on the order of an AU. In any case, the advantage for such strategies goes to the distal orbital forces (over the proximal). For example, forces in a 1 AU orbit will be able to achieve a maximum spread of about 55° against forces in a 2 AU orbit. Let's assume that the defending vessel has a forward slope of armour 10° off the center line, and the vessel is oriented to counter an attack from known forces at point A, giving maximum advantage to the hidden forces at point B, opposite in orbit. At this configuration, the point B forces will still have to overcome an armour slope of 25° (from the perpendicular). Side armour becomes available, but this is at 35°. This does not take into account secondary axial sloping... so it is a best case for the attackers.Yes, everything becomes much easier as ranges close.

I realise that your diagram is over simplified. Not sure if you quite understood my point, but I will assume you have.

Right, so I got some words about this, and the stealth in space section. I don't think that "stealth in space is impossible" is accurate - especially in crowded orbital space - but I do think that it's accurate to say something like "there are no stealthy interplanetary maneuvers".

Fundamentally, the problem is that the time something needs to be in motion is very long, which means that sensors have, effectively, a lot of time to locate something. The people attempting to detect incoming spacecraft are not morons, will probably have lots of options, will probably know at least approximately where to look from the very beginning, and will generally be able to scale sensor capability faster than the technological limits on stealth can be overcome by simply stacking bigger sensors and more processing capability. There's almost no way around this problem insofar as, the faster you want to get somewhere, the brighter and longer you need to burn. Anything fast enough to take advantage of stealth is too bright to be stealthy, anything cold enough to be stealthy can't get anywhere in time to use it.

This makes the risk-reward ratio for pulling off stealth is lopsided in favor of risk. This isn't quite 'everyone sees everything', and you can disguise exact loadouts, payloads, etc - but you can't assume than anything you're doing isn't being seen by the enemy. It probably is, and given the timescales and fuel constraints on spacecraft, any spacecraft launched are made with this in mind. Once detected, there's no taking it back, and everyone can see you. This also factors into political and strategic calculus. Giving yourself days of non-detection in a months long voyage is close to useless. Taking months to get to your destination is useless if the political/military situation changes during month 3.

The goal of 'tough science fiction' is to create options, not restrictions, but I think with stealth in space, you've spent too much time trying to provide justification to fall back on established 'space is an ocean' tropes. Providing options means taking a hard look at what the science actually offers, and I think you basically spend the last half of your essay saying that if you wave your hands with *these* magic words, then all of the USN-in-space stuff is perfectly reasonable.

2) It is still possible to reach unexpected trajectories using a clearly visible initial burn by using a secondary 'stealth' drive. Examples include an ion engine or the hydrogen steamer concept further expanded upon by Isaac Kuo.

3) The amount of time it takes to travel between places in space is compensated for by the extreme volumes involved and the variety of more-or-less efficient trajectories you can choose from. The exact point of balance is up to the author.

4) The reward for stealth depends on the dominant weapon system and the balance between offence and defense in the setting. If missiles can wipe out a spaceship with a single hit, then stealth bombers reign supreme. If your lasers can be put into position to vaporize the enemy, then first strike capability is essential. If lasers need to whittle down the target over the course of hours, then stealth is pretty useless.

5) The pace of combat will resemble the age of sail, more or less, depending on the propulsion used. London-New York was a month, or a 0.005g Brachistochrone trajectory from Earth to Mars for 50km/s. A clipper from Plymouth (UK) to Syndey took over 100 days, which is achievable on an Earth-Mars route with only 25km/s. The upside of such a pace is that if you are detected a few weeks away from your objective, your opponent will not be able to do anything about it as their ships will take just as long to reach and defend it.

6) Contrivances and fitting the science to the story is the point of this blog.

"It is still possible to reach unexpected trajectories using a clearly visible initial burn by using a secondary 'stealth' drive. Examples include an ion engine or the hydrogen steamer concept further expanded upon by Isaac Kuo."

I wonder how hard it is to hide the initial burn. Here's how I would try it:

Build a giant, hollow spherical space station with an independently rotating catapult inside. Walls are just thick enough to hide what's happening inside, and covered with doors/ports.The catapult launch is the initial burn - this is for unmanned crafts, unless you have a very, very large station, due to initial acceleration - and the craft goes through a random door. Doors in general show random activity so that one door activation is not standing out. Similarly, generators are constantly running so there is no difference in heat output and such.

The projectile itself is a stealth design like, for example, the aforementioned H2-boiler (Kuo Boiler?). The station is in a space you control, so you can make sure there is no close sensor that could get too much detail on the surface station activity.

If this design works (and feel free to shoot it down), this gives first-strike capability, so only an unchallenged dominant power could build it without risking triggering MAD.(This is why, historically, there were treaties to limit ABM tech, as a working antimissile shield would give you first strike capability, forcing the other side to attack before your shield is completed.)

Wait - big spherical station with an inner main gun, unstoppable attack, symbol of a military's unchallenged power, counts as WMD and would wipe an entire (habitat) world in one shot... Is that a hard-SF Death Star?

"The people attempting to detect incoming spacecraft are not morons, will probably have lots of options, will probably know at least approximately where to look from the very beginning, and will generally be able to scale sensor capability faster than the technological limits on stealth can be overcome by simply stacking bigger sensors and more processing capability."

All this is equally true for the F-117, the B-2, etc. Except: options are generally more limited in space, because you really only have radiation to work with (EM or particulate), and you need something that can search large volumes of space at incredible distances (which means you need incredible sensitivity); and, there are practical limitations to how much you can continue to stack bigger sensors and processing capabilities (which you need a lot more of).

There's almost no way around this problem insofar as, the faster "you want to get somewhere, the brighter and longer you need to burn. Anything fast enough to take advantage of stealth is too bright to be stealthy, anything cold enough to be stealthy can't get anywhere in time to use it."

Depends upon how much acceleration you really need. You can get "fast" with long-term low acceleration... ion engines that are REALLY difficult to detect.

"Once detected, there's no taking it back, and everyone can see you."

This is simply not true. Detection is one thing, tracking is another. Unless you actually have a track, it is fairly easy to get lost again.

"This also factors into political and strategic calculus. Giving yourself days of non-detection in a months long voyage is close to useless. Taking months to get to your destination is useless if the political/military situation changes during month 3."

Depends a lot upon if you are talking about strategic or tactical stealth. A few days, or even a few minutes, of stealth can be VERY effective if you are using that time to deploy sensors, mines, equipment, weapons platforms, kinetic weapons, etc. For that matter, your statement is not enitrely valid, because strategic planners generally have built in contingencies.

Depends. There ARE means to hide the initial burn, depending upon the sensor capabilities of the enemy. First, commit the burn behind an object. If the enemy surrounds you, you might be out of luck; otherwise, it is not so easy for someone to simply put an observation post in a distal orbit when it means crossing an orbital space that you control. There is also the option of using low energy concentration and/or high vector control burns. The enemy can only analyse the burn if they can detect the burn. That is not always a given, especially with ion thrust. You could also use a flattened plume, which is how the F-117 controls emission heat from its plume. Another option is to use an "impure" burn. If you have different engines burning different propellants at different rates, and mix the exhaust, it can be virtually impossible to analyse, even if it IS detected.

"Build a giant, hollow spherical space station with an independently rotating catapult inside. Walls are just thick enough to hide what's happening inside, and covered with doors/ports.The catapult launch is the initial burn - this is for unmanned crafts, unless you have a very, very large station, due to initial acceleration - and the craft goes through a random door. Doors in general show random activity so that one door activation is not standing out. Similarly, generators are constantly running so there is no difference in heat output and such."

A disk would be much less expensive. Also, there is no reason to have the catapult rotating independently, but that is fine if you want.Some thoughts/questions regarding the catapults: Are you intending to use the centrifugal force for launch? Yes, this would be effective... but no need to use doors. Just hang the launch from the outside of the catapult, and release. For an added boost, you could construct an EM catapult track on a section of the centrifuge arm. You get a base velocity from the angular momentum of the centrifuge, but you can add velocity to this using the EM track.

I assume there is a full sensor net around because:- Great powers would put one in place and you can't do much about it before the shooting starts- Once the shooting starts, sensor platforms are the easiest things to hide/camouflage/use someone else's, so it is not safe to bet on missing none- If it works against a sensor net, it works against no sensor net anyway

For the catapult, I was thinking about a high-acceleration cannon, something like a railgun, coilgun, light-gas gun... According to Wikipedia, today's artillery shell electronics are rated for 15500g, and it doesn't seem far-fetched to imagine the craft to be made to withstand that kind of acceleration. (Obviously, it is unmanned, but then again, so are space probes and ICBMs)With a 500m catapult, it would give 12+km/s of delta-V. 500m seems pretty reasonable to me for a catapult and its hiding sphere for a major system power.If we don't actually need much for the hiding sphere, it stops being a determinant factor. For example, with 10kg/m² (equivalent of a ~4mm thick aluminium plate), a 10km-diameter sphere would mass about 3000t, or the mass of a Saturn V. At this point, the catapult itself is probably the biggest industrial challenge. At 15500g, this would be 55+km/s, which is more than enough for anything in this system unless the station was in low Solar orbit - but a catapult capable of delivering 15500g of acceleration over 10km may be a bit too much of a monster to build anyway. Maybe we'd simply go for the best catapult we can build and then see how thick a sphere we can build around it with what's left of the budget.

About the doors and the catapult rotating independently, this is because otherwise the other side(s) will look at it and guess where the exit is, even at a distance - meaning they will know where it is aiming. It is not quite enough to calculate trajectories, as they will not know the delta-V of the boost (nor which one, if any, of the potential launches is a real one and which ones are fake and door-test ones), but it is enough to give them some serious guesses, which is more than I'd want them to.

"I assume there is a full sensor net around because:- Great powers would put one in place and you can't do much about it before the shooting starts- Once the shooting starts, sensor platforms are the easiest things to hide/camouflage/use someone else's, so it is not safe to bet on missing none- If it works against a sensor net, it works against no sensor net anyway"

That's not really given. If two planets are preparing to turn a cold war into a hot one, they might spend a lot of time and resources tracking down and pointing a laser at every sensor around their planet. The moment the war is declared, the vast majority of those sensors go up in flames.

It can happen beforehand too. It might become a diplomatic matter if sensors from an unfriendly nation are found orbiting your home planet. Allowing them to be there becomes a matter of trust. The politics involved might resemble missile launchers being moved closer to borders during the Cold War of the 60s.

While it is not a given, it doesn't seem safe to count on its absence, or even to count on getting rid of it.

Even if we try shooting it down with the opening salvo, the same salvo can also target other installations and objectives. Even more, if sensors are on a distant orbit, they may take longer to shoot down. Even hiding weapons close by will be hard to do for all of the sensor platforms.So the opening salvo will be made under a full sensor net anyway.

Then, even if one side manages to get rid of most of the other side's sensor net, the other side only needs a few working sensors here and there to still see what's going on. And the attackers can't know how many, what kind of or where those remaining sensors are, or they would have probably shot them down as well.So while it may be worth it to degrade the other side's ability to see what's going on, it is not safe to assume they were blinded.

That said, I would indeed expect each side to have control of their home planet's hill sphere, and the other side to not have high-end sensors here - and the sensors they do have would probably not last long: at this range, they would effectively be instantly shot down once discovered.It may still be possible to get high-end sensors around enemy home planets through subterfuge, particularly before hostilities, though "freighters" or "commercial satellites", for example. The next step being placing weapons, but this may be (even) harder and more politically risky.

My point is, even if one side can (eventually) get rid of the other side's sensor coverage once the shooting starts, and will probably try it (as it will still give significant advantages), they can't rely on it.

Fewer numbers of sensors means either their owners accept much longer scan times, or decide to completely ignore certain volumes of space. Either of these gives a chance for stealth ships to leave orbit.

Another thing is that trying to find a nearby satellite when you have an entire planet's worth of power is not so hard. Bathe everything in X-rays. Any unidentified echo return is tagged as a hostile. I doubt sensor platforms tailored for visual and infrared stealth can do anything about a wave of x-ray radiation.

Most importantly, the fact that we're having this debate means that the combat has become interesting! Absolute certainties make for predictable outcomes. Stories thrive in uncertain and unpredictable settings.

Even without stealth, a missile attack might require a sphere for defense (to make sure maximum surface area/firepower is provided ), and a concentrated attack would require a wall that can 'flex' to provide weapons fire at the required ranges and targets.

Nonetheless, how might engine power/propellant reserve detirmine the formation used? How much might a formation be able to shift between wall and sphere? I presume all of this depends on how dispersed your formation is, whether you can get away with a tight knit grouping. A formation that requires extreme dispersion to avoid flanking and a concentrated barrage/minimised turret traverse time might have difficulty changing formations.

I was going to concentrate of missile and kinetics in Part III, but they're not enough for an entire post, so I'm leaving Part III for later, once I have more to say.

As for your question, the defensive formation to use against missiles is determined by, in order of importance: how early they are detected, how you shoot them down, and how deadly they are.

If you detect them very late, then it is essential to concentrate your ships so that they can focus their defensive fire on each missile, and cover each other's blind spots. If you use lasers, then you need a geometric arrangement to give each defensive turret a clear line of sight. If you use anti-missile missiles, you need to make sure each AMM can reach its target in time. If the missiles are not very deadly, then they will be sent out in mass attacks against a single target, so you will arrange your fleet to expose the defensive ships as they are the least likely to be targeted, while keeping the valuable ships in a clearly defended position.